%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG219+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:58:45 AM UTC 2025
% Result : Theorem 0.22s 0.56s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ALG219+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Jun 19 10:49:09 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.22/0.56 % SZS status Theorem
% 0.22/0.56 % SZS output start Proof
% 0.22/0.56 tff(g1_vectsp_2_type, type, (
% 0.22/0.56 g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.22/0.56 tff(u1_vectsp_2_type, type, (
% 0.22/0.56 u1_vectsp_2: ( $i * $i ) > $i)).
% 0.22/0.56 tff(tptp_fun_B_1_type, type, (
% 0.22/0.56 tptp_fun_B_1: $i)).
% 0.22/0.56 tff(tptp_fun_A_0_type, type, (
% 0.22/0.56 tptp_fun_A_0: $i)).
% 0.22/0.56 tff(u2_struct_0_type, type, (
% 0.22/0.56 u2_struct_0: $i > $i)).
% 0.22/0.56 tff(u1_rlvect_1_type, type, (
% 0.22/0.56 u1_rlvect_1: $i > $i)).
% 0.22/0.56 tff(u1_struct_0_type, type, (
% 0.22/0.56 u1_struct_0: $i > $i)).
% 0.22/0.56 tff(k1_rmod_5_type, type, (
% 0.22/0.56 k1_rmod_5: ( $i * $i * $i ) > $i)).
% 0.22/0.56 tff(l1_struct_0_type, type, (
% 0.22/0.56 l1_struct_0: $i > $o)).
% 0.22/0.56 tff(l2_struct_0_type, type, (
% 0.22/0.56 l2_struct_0: $i > $o)).
% 0.22/0.56 tff(l1_rlvect_1_type, type, (
% 0.22/0.56 l1_rlvect_1: $i > $o)).
% 0.22/0.56 tff(l2_vectsp_1_type, type, (
% 0.22/0.56 l2_vectsp_1: $i > $o)).
% 0.22/0.56 tff(l3_vectsp_1_type, type, (
% 0.22/0.56 l3_vectsp_1: $i > $o)).
% 0.22/0.56 tff(l1_vectsp_2_type, type, (
% 0.22/0.56 l1_vectsp_2: ( $i * $i ) > $o)).
% 0.22/0.56 tff(v5_vectsp_2_type, type, (
% 0.22/0.56 v5_vectsp_2: ( $i * $i ) > $o)).
% 0.22/0.56 tff(v3_vectsp_2_type, type, (
% 0.22/0.56 v3_vectsp_2: ( $i * $i ) > $o)).
% 0.22/0.56 tff(v6_rlvect_1_type, type, (
% 0.22/0.56 v6_rlvect_1: $i > $o)).
% 0.22/0.56 tff(v5_rlvect_1_type, type, (
% 0.22/0.56 v5_rlvect_1: $i > $o)).
% 0.22/0.56 tff(v4_rlvect_1_type, type, (
% 0.22/0.56 v4_rlvect_1: $i > $o)).
% 0.22/0.56 tff(v3_rlvect_1_type, type, (
% 0.22/0.56 v3_rlvect_1: $i > $o)).
% 0.22/0.56 tff(v3_struct_0_type, type, (
% 0.22/0.56 v3_struct_0: $i > $o)).
% 0.22/0.56 tff(m1_subset_1_type, type, (
% 0.22/0.56 m1_subset_1: ( $i * $i ) > $o)).
% 0.22/0.56 tff(k1_zfmisc_1_type, type, (
% 0.22/0.56 k1_zfmisc_1: $i > $i)).
% 0.22/0.56 tff(k2_group_1_type, type, (
% 0.22/0.56 k2_group_1: $i > $i)).
% 0.22/0.56 tff(k1_rlvect_1_type, type, (
% 0.22/0.56 k1_rlvect_1: $i > $i)).
% 0.22/0.56 tff(v2_vectsp_2_type, type, (
% 0.22/0.56 v2_vectsp_2: $i > $o)).
% 0.22/0.56 tff(v10_vectsp_1_type, type, (
% 0.22/0.56 v10_vectsp_1: $i > $o)).
% 0.22/0.56 tff(v8_vectsp_1_type, type, (
% 0.22/0.56 v8_vectsp_1: $i > $o)).
% 0.22/0.56 tff(v7_vectsp_1_type, type, (
% 0.22/0.56 v7_vectsp_1: $i > $o)).
% 0.22/0.56 tff(v6_vectsp_1_type, type, (
% 0.22/0.56 v6_vectsp_1: $i > $o)).
% 0.22/0.56 tff(v7_group_1_type, type, (
% 0.22/0.56 v7_group_1: $i > $o)).
% 0.22/0.56 tff(v4_group_1_type, type, (
% 0.22/0.56 v4_group_1: $i > $o)).
% 0.22/0.56 tff(m1_rmod_2_type, type, (
% 0.22/0.56 m1_rmod_2: ( $i * $i * $i ) > $o)).
% 0.22/0.56 tff(k2_rmod_2_type, type, (
% 0.22/0.56 k2_rmod_2: ( $i * $i ) > $i)).
% 0.22/0.56 tff(1,plain,
% 0.22/0.56 (^[A: $i] : refl(((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(2,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.56 tff(3,plain,
% 0.22/0.56 (^[A: $i] : rewrite(((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(4,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.56 tff(5,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(6,plain,
% 0.22/0.56 (^[A: $i] : rewrite((l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(7,plain,
% 0.22/0.56 (![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A))) <=> ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.56 tff(8,axiom,(![A: $i] : (l3_vectsp_1(A) => (l1_rlvect_1(A) & l2_vectsp_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_vectsp_1')).
% 0.22/0.56 tff(9,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.56 tff(10,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.56 tff(11,plain,(
% 0.22/0.56 ![A: $i] : ((~l3_vectsp_1(A)) | (l1_rlvect_1(A) & l2_vectsp_1(A)))),
% 0.22/0.56 inference(skolemize,[status(sab)],[10])).
% 0.22/0.56 tff(12,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.56 tff(13,plain,
% 0.22/0.56 (![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.22/0.56 tff(14,plain,
% 0.22/0.56 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(15,plain,
% 0.22/0.56 ((~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))))) <=> (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(16,plain,
% 0.22/0.56 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))))) <=> (((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))))))),
% 0.22/0.56 inference(monotonicity,[status(thm)],[15])).
% 0.22/0.56 tff(17,plain,
% 0.22/0.56 ((((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0)) & (~((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))))) <=> ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))))))),
% 0.22/0.56 inference(transitivity,[status(thm)],[16, 14])).
% 0.22/0.56 tff(18,plain,
% 0.22/0.56 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(19,plain,
% 0.22/0.56 ((~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ((C = u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(20,axiom,(~![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v3_vectsp_2(B, A)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ((C = u1_struct_0(B)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t14_rmod_5')).
% 0.22/0.56 tff(21,plain,
% 0.22/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.22/0.56 tff(22,plain,
% 0.22/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.22/0.56 tff(23,plain,
% 0.22/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.22/0.56 tff(24,plain,
% 0.22/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(B)))) | (k1_rmod_5(A, B, u1_struct_0(B)) = B) | (k1_rlvect_1(A) = k2_group_1(A)) | (~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v3_vectsp_2(B, A) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.22/0.56 tff(25,plain,
% 0.22/0.56 ((~v3_struct_0(A!0)) & v3_rlvect_1(A!0) & v4_rlvect_1(A!0) & v5_rlvect_1(A!0) & v6_rlvect_1(A!0) & v4_group_1(A!0) & v7_group_1(A!0) & v6_vectsp_1(A!0) & v7_vectsp_1(A!0) & v8_vectsp_1(A!0) & (~v10_vectsp_1(A!0)) & v2_vectsp_2(A!0) & l3_vectsp_1(A!0) & (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.22/0.56 tff(26,plain,
% 0.22/0.56 (l3_vectsp_1(A!0)),
% 0.22/0.56 inference(and_elim,[status(thm)],[25])).
% 0.22/0.56 tff(27,plain,
% 0.22/0.56 (((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))) <=> ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(28,plain,
% 0.22/0.56 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | ((~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(29,plain,
% 0.22/0.56 ((~![A: $i] : ((~l3_vectsp_1(A)) | (~((~l1_rlvect_1(A)) | (~l2_vectsp_1(A)))))) | (~l3_vectsp_1(A!0)) | (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.56 tff(30,plain,
% 0.22/0.56 (~((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0)))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.22/0.56 tff(31,plain,
% 0.22/0.56 (((~l1_rlvect_1(A!0)) | (~l2_vectsp_1(A!0))) | l1_rlvect_1(A!0)),
% 0.22/0.56 inference(tautology,[status(thm)],[])).
% 0.22/0.56 tff(32,plain,
% 0.22/0.56 (l1_rlvect_1(A!0)),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.22/0.56 tff(33,plain,
% 0.22/0.56 (^[A: $i] : refl((l2_struct_0(A) | (~l1_rlvect_1(A))) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(34,plain,
% 0.22/0.56 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[33])).
% 0.22/0.56 tff(35,plain,
% 0.22/0.56 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A))) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(36,plain,
% 0.22/0.56 (^[A: $i] : rewrite((l1_rlvect_1(A) => l2_struct_0(A)) <=> (l2_struct_0(A) | (~l1_rlvect_1(A))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(37,plain,
% 0.22/0.56 (![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A)) <=> ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[36])).
% 0.22/0.56 tff(38,axiom,(![A: $i] : (l1_rlvect_1(A) => l2_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_rlvect_1')).
% 0.22/0.56 tff(39,plain,
% 0.22/0.56 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.56 tff(40,plain,
% 0.22/0.56 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.22/0.56 tff(41,plain,(
% 0.22/0.56 ![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(skolemize,[status(sab)],[40])).
% 0.22/0.56 tff(42,plain,
% 0.22/0.56 (![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.22/0.56 tff(43,plain,
% 0.22/0.56 (((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))) <=> ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(44,plain,
% 0.22/0.56 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | (l2_struct_0(A!0) | (~l1_rlvect_1(A!0)))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(45,plain,
% 0.22/0.56 ((~![A: $i] : (l2_struct_0(A) | (~l1_rlvect_1(A)))) | l2_struct_0(A!0) | (~l1_rlvect_1(A!0))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.22/0.56 tff(46,plain,
% 0.22/0.56 (l2_struct_0(A!0)),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[45, 42, 32])).
% 0.22/0.56 tff(47,plain,
% 0.22/0.56 (^[A: $i] : refl((l1_struct_0(A) | (~l2_struct_0(A))) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(48,plain,
% 0.22/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.56 tff(49,plain,
% 0.22/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(50,plain,
% 0.22/0.56 (^[A: $i] : rewrite((l2_struct_0(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_struct_0(A))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(51,plain,
% 0.22/0.56 (![A: $i] : (l2_struct_0(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.56 tff(52,axiom,(![A: $i] : (l2_struct_0(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_struct_0')).
% 0.22/0.56 tff(53,plain,
% 0.22/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.56 tff(54,plain,
% 0.22/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.22/0.56 tff(55,plain,(
% 0.22/0.56 ![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(skolemize,[status(sab)],[54])).
% 0.22/0.56 tff(56,plain,
% 0.22/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.22/0.56 tff(57,plain,
% 0.22/0.56 (((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(58,plain,
% 0.22/0.56 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | (l1_struct_0(A!0) | (~l2_struct_0(A!0)))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(59,plain,
% 0.22/0.56 ((~![A: $i] : (l1_struct_0(A) | (~l2_struct_0(A)))) | l1_struct_0(A!0) | (~l2_struct_0(A!0))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.56 tff(60,plain,
% 0.22/0.56 (l1_struct_0(A!0)),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[59, 56, 46])).
% 0.22/0.56 tff(61,plain,
% 0.22/0.56 (^[A: $i, B: $i] : refl(((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(62,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[61])).
% 0.22/0.56 tff(63,plain,
% 0.22/0.56 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1_struct_0(A) & l1_vectsp_2(B, A)) <=> (~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))), ((~(l1_struct_0(A) & l1_vectsp_2(B, A))) <=> (~(~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))))), rewrite((~(~((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))) <=> ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))), ((~(l1_struct_0(A) & l1_vectsp_2(B, A))) <=> ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A))))), (((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))))), rewrite(((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | ((~l1_struct_0(A)) | (~l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))), (((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(64,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[63])).
% 0.22/0.56 tff(65,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A)))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(66,plain,
% 0.22/0.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))), (((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((l1_struct_0(A) & l1_vectsp_2(B, A)) => ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))))), rewrite(((l1_struct_0(A) & l1_vectsp_2(B, A)) => ((~v3_vectsp_2(B, A)) | (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))), (((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(67,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[66])).
% 0.22/0.56 tff(68,axiom,(![A: $i, B: $i] : ((l1_struct_0(A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(B, A) => (B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_vectsp_2')).
% 0.22/0.56 tff(69,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.56 tff(70,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.22/0.56 tff(71,plain,(
% 0.22/0.56 ![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~(l1_struct_0(A) & l1_vectsp_2(B, A))))),
% 0.22/0.56 inference(skolemize,[status(sab)],[70])).
% 0.22/0.56 tff(72,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.22/0.56 tff(73,plain,
% 0.22/0.56 (![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.22/0.56 tff(74,plain,
% 0.22/0.56 (~((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) | (~((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0))))),
% 0.22/0.56 inference(and_elim,[status(thm)],[25])).
% 0.22/0.56 tff(75,plain,
% 0.22/0.56 ((~v3_struct_0(B!1)) & v3_rlvect_1(B!1) & v4_rlvect_1(B!1) & v5_rlvect_1(B!1) & v6_rlvect_1(B!1) & v3_vectsp_2(B!1, A!0) & v5_vectsp_2(B!1, A!0) & l1_vectsp_2(B!1, A!0)),
% 0.22/0.56 inference(or_elim,[status(thm)],[74])).
% 0.22/0.56 tff(76,plain,
% 0.22/0.56 (l1_vectsp_2(B!1, A!0)),
% 0.22/0.56 inference(and_elim,[status(thm)],[75])).
% 0.22/0.56 tff(77,plain,
% 0.22/0.56 (v3_vectsp_2(B!1, A!0)),
% 0.22/0.56 inference(and_elim,[status(thm)],[75])).
% 0.22/0.56 tff(78,plain,
% 0.22/0.56 (((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(79,plain,
% 0.22/0.56 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | ((B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0)))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(80,plain,
% 0.22/0.56 ((~![A: $i, B: $i] : ((B = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~v3_vectsp_2(B, A)) | (~l1_vectsp_2(B, A)) | (~l1_struct_0(A)))) | (B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~v3_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (~l1_struct_0(A!0))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.22/0.56 tff(81,plain,
% 0.22/0.56 ((B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) | (~l1_struct_0(A!0))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[80, 77, 76, 73])).
% 0.22/0.56 tff(82,plain,
% 0.22/0.56 (B!1 = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[81, 60])).
% 0.22/0.56 tff(83,plain,
% 0.22/0.56 (g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)) = B!1),
% 0.22/0.56 inference(symmetry,[status(thm)],[82])).
% 0.22/0.56 tff(84,plain,
% 0.22/0.56 ((k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) <=> (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1)),
% 0.22/0.56 inference(monotonicity,[status(thm)],[83])).
% 0.22/0.56 tff(85,plain,
% 0.22/0.56 ((k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1) <=> (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.22/0.56 inference(symmetry,[status(thm)],[84])).
% 0.22/0.56 tff(86,plain,
% 0.22/0.56 ((~(k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1)) <=> (~(k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.22/0.56 inference(monotonicity,[status(thm)],[85])).
% 0.22/0.56 tff(87,plain,
% 0.22/0.56 (~(k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = B!1)),
% 0.22/0.56 inference(or_elim,[status(thm)],[74])).
% 0.22/0.56 tff(88,plain,
% 0.22/0.56 (~(k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.56 tff(89,plain,
% 0.22/0.56 (^[A: $i] : refl((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(90,plain,
% 0.22/0.56 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[89])).
% 0.22/0.57 tff(91,plain,
% 0.22/0.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(92,plain,
% 0.22/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[91])).
% 0.22/0.57 tff(93,plain,
% 0.22/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.22/0.57 inference(transitivity,[status(thm)],[92, 90])).
% 0.22/0.57 tff(94,plain,
% 0.22/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) <=> (~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))))), rewrite(((v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A))) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(95,plain,
% 0.22/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[94])).
% 0.22/0.57 tff(96,plain,
% 0.22/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(97,plain,
% 0.22/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(98,plain,
% 0.22/0.57 (![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[97])).
% 0.22/0.57 tff(99,axiom,(![A: $i] : (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_rmod_2')).
% 0.22/0.57 tff(100,plain,
% 0.22/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.22/0.57 tff(101,plain,
% 0.22/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.22/0.57 tff(102,plain,(
% 0.22/0.57 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B)))))),
% 0.22/0.57 inference(skolemize,[status(sab)],[101])).
% 0.22/0.57 tff(103,plain,
% 0.22/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.22/0.57 tff(104,plain,
% 0.22/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.22/0.57 tff(105,plain,
% 0.22/0.57 (v8_vectsp_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(106,plain,
% 0.22/0.57 (v7_vectsp_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(107,plain,
% 0.22/0.57 (v6_vectsp_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(108,plain,
% 0.22/0.57 (v4_group_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(109,plain,
% 0.22/0.57 (v6_rlvect_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(110,plain,
% 0.22/0.57 (v5_rlvect_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(111,plain,
% 0.22/0.57 (v4_rlvect_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(112,plain,
% 0.22/0.57 (v3_rlvect_1(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(113,plain,
% 0.22/0.57 (~v3_struct_0(A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[25])).
% 0.22/0.57 tff(114,plain,
% 0.22/0.57 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(115,plain,
% 0.22/0.57 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) <=> (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(116,plain,
% 0.22/0.57 (^[B: $i] : rewrite((v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(117,plain,
% 0.22/0.57 (![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[116])).
% 0.22/0.57 tff(118,plain,
% 0.22/0.57 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)))) <=> (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.22/0.57 inference(monotonicity,[status(thm)],[117])).
% 0.22/0.57 tff(119,plain,
% 0.22/0.57 ((v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)))) <=> (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.22/0.57 inference(transitivity,[status(thm)],[118, 115])).
% 0.22/0.57 tff(120,plain,
% 0.22/0.57 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | (v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))))),
% 0.22/0.57 inference(monotonicity,[status(thm)],[119])).
% 0.22/0.57 tff(121,plain,
% 0.22/0.57 (((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B)))))),
% 0.22/0.57 inference(transitivity,[status(thm)],[120, 114])).
% 0.22/0.57 tff(122,plain,
% 0.22/0.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | (v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0))))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.57 tff(123,plain,
% 0.22/0.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | ![B: $i] : (v3_struct_0(B) | (k2_rmod_2(A, B) = g1_vectsp_2(A, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A, B))) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.22/0.57 tff(124,plain,
% 0.22/0.57 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[123, 113, 112, 111, 110, 109, 108, 107, 106, 105, 26, 104])).
% 0.22/0.57 tff(125,plain,
% 0.22/0.57 (v5_vectsp_2(B!1, A!0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[75])).
% 0.22/0.57 tff(126,plain,
% 0.22/0.57 (v6_rlvect_1(B!1)),
% 0.22/0.57 inference(and_elim,[status(thm)],[75])).
% 0.22/0.57 tff(127,plain,
% 0.22/0.57 (v5_rlvect_1(B!1)),
% 0.22/0.57 inference(and_elim,[status(thm)],[75])).
% 0.22/0.57 tff(128,plain,
% 0.22/0.57 (v4_rlvect_1(B!1)),
% 0.22/0.57 inference(and_elim,[status(thm)],[75])).
% 0.22/0.57 tff(129,plain,
% 0.22/0.57 (v3_rlvect_1(B!1)),
% 0.22/0.57 inference(and_elim,[status(thm)],[75])).
% 0.22/0.57 tff(130,plain,
% 0.22/0.57 (~v3_struct_0(B!1)),
% 0.22/0.57 inference(and_elim,[status(thm)],[75])).
% 0.22/0.57 tff(131,plain,
% 0.22/0.57 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(132,plain,
% 0.22/0.58 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(133,plain,
% 0.22/0.58 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))))),
% 0.22/0.58 inference(monotonicity,[status(thm)],[132])).
% 0.22/0.58 tff(134,plain,
% 0.22/0.58 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.22/0.58 inference(transitivity,[status(thm)],[133, 131])).
% 0.22/0.58 tff(135,plain,
% 0.22/0.58 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.22/0.58 inference(quant_inst,[status(thm)],[])).
% 0.22/0.58 tff(136,plain,
% 0.22/0.58 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | (k2_rmod_2(A!0, B) = g1_vectsp_2(A!0, u1_struct_0(B), u1_rlvect_1(B), u2_struct_0(B), u1_vectsp_2(A!0, B))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.22/0.58 tff(137,plain,
% 0.22/0.58 (k2_rmod_2(A!0, B!1) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))),
% 0.22/0.58 inference(unit_resolution,[status(thm)],[136, 130, 129, 128, 127, 126, 125, 76, 124])).
% 0.22/0.58 tff(138,plain,
% 0.22/0.58 (g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)) = k2_rmod_2(A!0, B!1)),
% 0.22/0.58 inference(symmetry,[status(thm)],[137])).
% 0.22/0.58 tff(139,plain,
% 0.22/0.58 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1) <=> m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)),
% 0.22/0.58 inference(monotonicity,[status(thm)],[138])).
% 0.22/0.58 tff(140,plain,
% 0.22/0.58 (m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1) <=> m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)),
% 0.22/0.58 inference(symmetry,[status(thm)],[139])).
% 0.22/0.58 tff(141,plain,
% 0.22/0.58 (^[A: $i, B: $i] : refl((v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(142,plain,
% 0.22/0.58 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[141])).
% 0.22/0.58 tff(143,plain,
% 0.22/0.58 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A))))))), rewrite((~(~(v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A))))), rewrite((v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)) <=> (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ((v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A))) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))))), rewrite(((v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A))) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B))))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(144,plain,
% 0.22/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[143])).
% 0.22/0.58 tff(145,plain,
% 0.22/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(146,plain,
% 0.22/0.58 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B))))), (((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B))) & v3_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B))) & v3_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B))), (((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B)))), ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)))), (((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), (((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))), (((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.44/0.58 inference(bind,[status(th)],[])).
% 0.44/0.58 tff(147,plain,
% 0.44/0.58 (![A: $i, B: $i] : ((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.44/0.58 inference(quant_intro,[status(thm)],[146])).
% 0.44/0.58 tff(148,axiom,(![A: $i, B: $i] : ((((((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & l3_vectsp_1(A)) & (~v3_struct_0(B))) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_rmod_2')).
% 0.44/0.58 tff(149,plain,
% 0.44/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.44/0.58 tff(150,plain,
% 0.44/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.44/0.58 tff(151,plain,(
% 0.44/0.58 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & (~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | (v3_vectsp_2(k2_rmod_2(A, B), A) & m1_rmod_2(k2_rmod_2(A, B), A, B)))),
% 0.44/0.58 inference(skolemize,[status(sab)],[150])).
% 0.44/0.58 tff(152,plain,
% 0.44/0.58 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.44/0.58 tff(153,plain,
% 0.44/0.58 (![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))),
% 0.44/0.58 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.44/0.58 tff(154,plain,
% 0.44/0.58 (((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(155,plain,
% 0.44/0.58 ((v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))))) <=> (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))),
% 0.44/0.58 inference(rewrite,[status(thm)],[])).
% 0.44/0.58 tff(156,plain,
% 0.44/0.58 (((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))))))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[155])).
% 0.44/0.59 tff(157,plain,
% 0.44/0.59 (((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[156, 154])).
% 0.44/0.59 tff(158,plain,
% 0.44/0.59 ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | (v3_struct_0(B!1) | v3_struct_0(A!0) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))))),
% 0.44/0.59 inference(quant_inst,[status(thm)],[])).
% 0.44/0.59 tff(159,plain,
% 0.44/0.59 ((~![A: $i, B: $i] : (v3_struct_0(B) | v3_struct_0(A) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v6_vectsp_1(A)) | (~v7_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~l3_vectsp_1(A)) | (~((~v3_vectsp_2(k2_rmod_2(A, B), A)) | (~m1_rmod_2(k2_rmod_2(A, B), A, B)))))) | v3_struct_0(A!0) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))))),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.44/0.59 tff(160,plain,
% 0.44/0.59 (~((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)))),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[159, 113, 112, 111, 110, 109, 108, 107, 106, 105, 26, 130, 129, 128, 127, 126, 125, 76, 153])).
% 0.44/0.59 tff(161,plain,
% 0.44/0.59 (((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))) | m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(162,plain,
% 0.44/0.59 (m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.44/0.59 tff(163,plain,
% 0.44/0.59 (m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[162, 140])).
% 0.44/0.59 tff(164,plain,
% 0.44/0.59 (v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0) <=> v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)),
% 0.44/0.59 inference(monotonicity,[status(thm)],[138])).
% 0.44/0.59 tff(165,plain,
% 0.44/0.59 (v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0) <=> v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)),
% 0.44/0.59 inference(symmetry,[status(thm)],[164])).
% 0.44/0.59 tff(166,plain,
% 0.44/0.59 (((~v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)) | (~m1_rmod_2(k2_rmod_2(A!0, B!1), A!0, B!1))) | v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)),
% 0.44/0.59 inference(tautology,[status(thm)],[])).
% 0.44/0.59 tff(167,plain,
% 0.44/0.59 (v3_vectsp_2(k2_rmod_2(A!0, B!1), A!0)),
% 0.44/0.59 inference(unit_resolution,[status(thm)],[166, 160])).
% 0.44/0.59 tff(168,plain,
% 0.44/0.59 (v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)),
% 0.44/0.59 inference(modus_ponens,[status(thm)],[167, 165])).
% 0.44/0.59 tff(169,plain,
% 0.44/0.59 (u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))) = u1_struct_0(k2_rmod_2(A!0, B!1))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[138])).
% 0.44/0.59 tff(170,plain,
% 0.44/0.59 (u1_struct_0(k2_rmod_2(A!0, B!1)) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.44/0.59 inference(symmetry,[status(thm)],[169])).
% 0.44/0.59 tff(171,plain,
% 0.44/0.59 (B!1 = k2_rmod_2(A!0, B!1)),
% 0.44/0.59 inference(transitivity,[status(thm)],[82, 138])).
% 0.44/0.59 tff(172,plain,
% 0.44/0.59 (u1_struct_0(B!1) = u1_struct_0(k2_rmod_2(A!0, B!1))),
% 0.44/0.59 inference(monotonicity,[status(thm)],[171])).
% 0.44/0.59 tff(173,plain,
% 0.44/0.59 (u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.44/0.59 inference(transitivity,[status(thm)],[172, 170])).
% 0.44/0.59 tff(174,plain,
% 0.44/0.59 (^[A: $i] : refl((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))),
% 0.44/0.59 inference(bind,[status(th)],[])).
% 0.44/0.59 tff(175,plain,
% 0.44/0.59 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.44/0.59 inference(quant_intro,[status(thm)],[174])).
% 0.44/0.59 tff(176,plain,
% 0.44/0.59 (^[A: $i] : rewrite((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))),
% 0.44/0.59 inference(bind,[status(th)],[])).
% 0.44/0.59 tff(177,plain,
% 0.44/0.59 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.44/0.59 inference(quant_intro,[status(thm)],[176])).
% 0.44/0.59 tff(178,plain,
% 0.44/0.59 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.44/0.59 inference(transitivity,[status(thm)],[177, 175])).
% 0.44/0.59 tff(179,plain,
% 0.44/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A)) <=> (~(v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) <=> (~(~(v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))))))), rewrite((~(~(v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)))), ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) <=> (~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))))), rewrite((~(~(v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)))), ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> ((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))), rewrite(((v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))), (((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> ((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))))), rewrite(((v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B)))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))), (((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))))),
% 0.44/0.59 inference(bind,[status(th)],[])).
% 0.44/0.59 tff(180,plain,
% 0.44/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> ![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.44/0.59 inference(quant_intro,[status(thm)],[179])).
% 0.44/0.59 tff(181,plain,
% 0.44/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.44/0.59 inference(rewrite,[status(thm)],[])).
% 0.44/0.59 tff(182,plain,
% 0.44/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A))), (((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A))), ((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A))), (((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v7_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A)) & v7_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A))), ((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A)))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A)) & v6_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A))), (((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A)))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A))), ((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A))), (((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)))), ((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A))))), (((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A))), (((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A)))), ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A)) & l3_vectsp_1(A)))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))), ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) <=> ((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B))), (((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B))), ((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A))), (((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))), ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) <=> ((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))) <=> ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))))), (((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))) <=> ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))))))), rewrite(((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))))) <=> ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))), (((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))) <=> ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))), (![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))) <=> ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))) <=> (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))), ((m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))) <=> (((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))), rewrite((((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))), (((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))) <=> ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))))), (![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))), (((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))))) <=> (((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))))), rewrite((((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))), (((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))))) <=> ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))))),
% 0.44/0.59 inference(bind,[status(th)],[])).
% 0.44/0.59 tff(183,plain,
% 0.44/0.59 (![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.44/0.59 inference(quant_intro,[status(thm)],[182])).
% 0.44/0.59 tff(184,axiom,(![A: $i] : ((((((((((((((~v3_struct_0(A)) & v3_rlvect_1(A)) & v4_rlvect_1(A)) & v5_rlvect_1(A)) & v6_rlvect_1(A)) & v4_group_1(A)) & v7_group_1(A)) & v6_vectsp_1(A)) & v7_vectsp_1(A)) & v8_vectsp_1(A)) & (~v10_vectsp_1(A))) & v2_vectsp_2(A)) & l3_vectsp_1(A)) => ![B: $i] : ((((((((~v3_struct_0(B)) & v3_rlvect_1(B)) & v4_rlvect_1(B)) & v5_rlvect_1(B)) & v6_rlvect_1(B)) & v5_vectsp_2(B, A)) & l1_vectsp_2(B, A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) => ![D: $i] : ((v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)) => ((C = u1_struct_0(D)) => ((k1_rlvect_1(A) = k2_group_1(A)) | (k1_rmod_5(A, B, C) = D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_rmod_5')).
% 0.44/0.59 tff(185,plain,
% 0.44/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.44/0.60 tff(186,plain,
% 0.44/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.44/0.60 tff(187,plain,(
% 0.44/0.60 ![A: $i] : ((~((~v3_struct_0(A)) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & (~v10_vectsp_1(A)) & v2_vectsp_2(A) & l3_vectsp_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B, A) & l1_vectsp_2(B, A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~(v3_vectsp_2(D, A) & m1_rmod_2(D, A, B)))))))),
% 0.44/0.60 inference(skolemize,[status(sab)],[186])).
% 0.44/0.60 tff(188,plain,
% 0.44/0.60 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.44/0.60 tff(189,plain,
% 0.44/0.60 (![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.44/0.60 tff(190,plain,
% 0.44/0.60 (v2_vectsp_2(A!0)),
% 0.44/0.60 inference(and_elim,[status(thm)],[25])).
% 0.44/0.60 tff(191,plain,
% 0.44/0.60 (~v10_vectsp_1(A!0)),
% 0.44/0.60 inference(and_elim,[status(thm)],[25])).
% 0.44/0.60 tff(192,plain,
% 0.44/0.60 (v7_group_1(A!0)),
% 0.44/0.60 inference(and_elim,[status(thm)],[25])).
% 0.44/0.60 tff(193,plain,
% 0.44/0.60 (((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))) <=> ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(194,plain,
% 0.44/0.60 ((v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(195,plain,
% 0.44/0.60 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))), (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))) <=> (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))), rewrite((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))), ((v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))) <=> (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))))),
% 0.46/0.60 inference(bind,[status(th)],[])).
% 0.46/0.60 tff(196,plain,
% 0.46/0.60 (![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))) <=> ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))),
% 0.46/0.60 inference(quant_intro,[status(thm)],[195])).
% 0.46/0.60 tff(197,plain,
% 0.46/0.60 ((v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[196])).
% 0.46/0.60 tff(198,plain,
% 0.46/0.60 ((v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) <=> (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[197, 194])).
% 0.46/0.60 tff(199,plain,
% 0.46/0.60 (((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))) <=> ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))))),
% 0.46/0.60 inference(monotonicity,[status(thm)],[198])).
% 0.46/0.60 tff(200,plain,
% 0.46/0.60 (((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))) <=> ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.46/0.60 inference(transitivity,[status(thm)],[199, 193])).
% 0.46/0.60 tff(201,plain,
% 0.46/0.60 ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | (v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~l3_vectsp_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~v7_group_1(A!0)) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A!0)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A!0, B, C) = D) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B))))))),
% 0.46/0.60 inference(quant_inst,[status(thm)],[])).
% 0.46/0.60 tff(202,plain,
% 0.46/0.60 ((~![A: $i] : (v10_vectsp_1(A) | v3_struct_0(A) | (~l3_vectsp_1(A)) | (~v6_vectsp_1(A)) | (~v8_vectsp_1(A)) | (~v7_group_1(A)) | (~v3_rlvect_1(A)) | (~v4_rlvect_1(A)) | (~v5_rlvect_1(A)) | (~v6_rlvect_1(A)) | (~v4_group_1(A)) | (~v7_vectsp_1(A)) | (~v2_vectsp_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_vectsp_2(B, A)) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((k1_rmod_5(A, B, C) = D) | (k1_rlvect_1(A) = k2_group_1(A)) | (~(C = u1_struct_0(D))) | (~v3_vectsp_2(D, A)) | (~m1_rmod_2(D, A, B))))))) | v10_vectsp_1(A!0) | v3_struct_0(A!0) | (~v3_rlvect_1(A!0)) | (~v4_rlvect_1(A!0)) | (~v5_rlvect_1(A!0)) | (~v6_rlvect_1(A!0)) | (~v4_group_1(A!0)) | (~v6_vectsp_1(A!0)) | (~v7_vectsp_1(A!0)) | (~v8_vectsp_1(A!0)) | (~l3_vectsp_1(A!0)) | (~v2_vectsp_2(A!0)) | (~v7_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))),
% 0.46/0.60 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.46/0.60 tff(203,plain,
% 0.46/0.60 (![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))),
% 0.46/0.60 inference(unit_resolution,[status(thm)],[202, 113, 112, 111, 110, 109, 108, 192, 107, 106, 105, 191, 190, 26, 189])).
% 0.46/0.60 tff(204,plain,
% 0.46/0.60 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(205,plain,
% 0.46/0.60 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.46/0.60 inference(rewrite,[status(thm)],[])).
% 0.46/0.60 tff(206,plain,
% 0.46/0.60 (^[C: $i] : rewrite(((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))) <=> ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.46/0.61 inference(bind,[status(th)],[])).
% 0.46/0.61 tff(207,plain,
% 0.46/0.61 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))),
% 0.46/0.61 inference(quant_intro,[status(thm)],[206])).
% 0.46/0.61 tff(208,plain,
% 0.46/0.61 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1))))) <=> (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[207])).
% 0.46/0.61 tff(209,plain,
% 0.46/0.61 ((v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1))))) <=> (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[208, 205])).
% 0.46/0.61 tff(210,plain,
% 0.46/0.61 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[209])).
% 0.46/0.61 tff(211,plain,
% 0.46/0.61 (((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D))))),
% 0.46/0.61 inference(transitivity,[status(thm)],[210, 204])).
% 0.46/0.61 tff(212,plain,
% 0.46/0.61 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | (v3_struct_0(B!1) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | (~l1_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B!1, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B!1)))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(213,plain,
% 0.46/0.61 ((~![B: $i] : (v3_struct_0(B) | (~v3_rlvect_1(B)) | (~v4_rlvect_1(B)) | (~v5_rlvect_1(B)) | (~v6_rlvect_1(B)) | (~v5_vectsp_2(B, A!0)) | (~l1_vectsp_2(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (k1_rmod_5(A!0, B, C) = D) | (~v3_vectsp_2(D, A!0)) | (~m1_rmod_2(D, A!0, B)))))) | v3_struct_0(B!1) | (~l1_vectsp_2(B!1, A!0)) | (~v3_rlvect_1(B!1)) | (~v4_rlvect_1(B!1)) | (~v5_rlvect_1(B!1)) | (~v6_rlvect_1(B!1)) | (~v5_vectsp_2(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.46/0.61 tff(214,plain,
% 0.46/0.61 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[213, 130, 129, 128, 127, 126, 125, 76, 203])).
% 0.46/0.61 tff(215,plain,
% 0.46/0.61 (m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))),
% 0.46/0.61 inference(or_elim,[status(thm)],[74])).
% 0.46/0.61 tff(216,plain,
% 0.46/0.61 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(217,plain,
% 0.46/0.61 (((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) <=> ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(218,plain,
% 0.46/0.61 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))))),
% 0.46/0.61 inference(monotonicity,[status(thm)],[217])).
% 0.46/0.61 tff(219,plain,
% 0.46/0.61 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.46/0.61 inference(transitivity,[status(thm)],[218, 216])).
% 0.46/0.61 tff(220,plain,
% 0.46/0.61 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | ((~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D)))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(221,plain,
% 0.46/0.61 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((~(C = u1_struct_0(D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (k1_rmod_5(A!0, B!1, C) = D)))) | (~m1_subset_1(u1_struct_0(B!1), k1_zfmisc_1(u1_struct_0(B!1)))) | ![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.46/0.61 tff(222,plain,
% 0.46/0.61 (![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))),
% 0.46/0.61 inference(unit_resolution,[status(thm)],[221, 215, 214])).
% 0.46/0.61 tff(223,plain,
% 0.46/0.61 (~(k1_rlvect_1(A!0) = k2_group_1(A!0))),
% 0.46/0.61 inference(or_elim,[status(thm)],[74])).
% 0.46/0.61 tff(224,plain,
% 0.46/0.61 (((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) <=> ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.46/0.61 inference(rewrite,[status(thm)],[])).
% 0.46/0.61 tff(225,plain,
% 0.46/0.61 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))),
% 0.46/0.61 inference(quant_inst,[status(thm)],[])).
% 0.46/0.61 tff(226,plain,
% 0.46/0.61 ((~![D: $i] : ((k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(D, A!0, B!1)) | (~v3_vectsp_2(D, A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(D))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = D))) | (k1_rlvect_1(A!0) = k2_group_1(A!0)) | (~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (~(u1_struct_0(B!1) = u1_struct_0(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1))))) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.46/0.61 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.46/0.61 tff(227,plain,
% 0.46/0.61 ((~m1_rmod_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0, B!1)) | (~v3_vectsp_2(g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)), A!0)) | (k1_rmod_5(A!0, B!1, u1_struct_0(B!1)) = g1_vectsp_2(A!0, u1_struct_0(B!1), u1_rlvect_1(B!1), u2_struct_0(B!1), u1_vectsp_2(A!0, B!1)))),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[226, 223, 222, 173])).
% 0.46/0.62 tff(228,plain,
% 0.46/0.62 ($false),
% 0.46/0.62 inference(unit_resolution,[status(thm)],[227, 168, 163, 88])).
% 0.46/0.62 % SZS output end Proof
% 0.46/0.62 % E exiting
%------------------------------------------------------------------------------